Implied odds of the pot — an important part of poker math pot

Translated with the help of AI. We apologize for any errors and would appreciate your help in correcting them.

First, read the article about the second criterion: pot odds in poker or how to calculate the profitability of a call

Often during the game, you will have an unmade hand with the ability to strengthen to a strong combination. You need certain cards to help you. These matching cards are called outs, and the odds of these cards coming out are called odds. Trying to assemble your combination can be profitable, and maybe even negative.

To figure out when to try to collect it, and when the game is not worth the candle, you need to understand two important mathematical criteria for playing poker, which are called the pot odds and the supposed pot odds. Estimated (potential) odds or implied odds are a possible win on future streets if you put together a strong combination. In other words, it is a parameter that takes into account possible future profits. Sometimes a call at a disadvantageous chance of the pot can bring significant profits on subsequent streets if you get one of your outs. And this also needs to be taken into account when trying to assemble your combination at a the long run. 

1. Calculation of potential pot odds

• Let's imagine that your villain put 200 chips on the turn in a 400 pot, leaving 500 chips on his stack. 

You still get 3 to 1 pot odds (25%), but this does not take into account the remaining 500 chips in the opponent's stack that you can win from him in case of calling your draw on the river. Given this additional factor, you risk 200 chips to win 600 and potentially another 500. It turns out that according to the concept of potential pot odds, you risk 200 to win 1100 with some certain probability. That is, the probability that the player will pay the remaining chips on the river, say, 33%. If we take this figure of 33% as a constant in this calculation (after all, this is a variable in fact, and it also needs to be found out), it turns out that out of the remaining 500 opponent's chips in the long the long run, we will win about 157 chips on the river.

1. 600 + 157 = 757 chips – pay 200 to win 757 chips.
2. 200 / 957 = 21% – so much equity we need, so that in such conditions it would be profitable for us to make this stake.

In the bare flush draw 18%, consequently, the call on the turn for us is negative in terms of mathematical expectation in this situation. In order for it to become a plus, we need our collected flush opponent to pay >50% of cases for all the remaining 500 chips. But if we are in a position in this hand, we still have a potential chance to win the hand with a bluff. If our flush still does not come, but the villain goes to the check on the river, we, being in position, can play the bluff all-in for these 500 chips and knock out the opponent. The profitability of this action must also be taken into account if you go into detailed nuances. This is such an interesting game – poker. 

2. Reverse implied odds

If you believe that you have the implied odds to equalize the bet, you should also evaluate your inverse implied odds or how often you will be left behind after receiving the expected combination (for example, on a paired board, your flush may lose to the full house). Do not forget that outs that strengthen you may give the opponent an older hand, or he may already have a combination against which your outs will not help. 

Like implied odds, inverse potential odds cannot be calculated mathematically precisely, since it requires an assessment of how your opponents will act on future streets. If the current pot odds are good, you can often continue to play even despite the inverse implied odds. But if the chances of the pot are unfavorable, and there are too many draw on the board, which can turn into a hand stronger than yours, you should try to get to the opening of cards as cheaply as possible or think about playing fold now. 

It is especially important to drastically reduce the consideration of implaid odds when collecting their draw on paired boards. Below we list the hands with which serious backward implied odds of the bank act. pot

Hands with backward presumed pot odds:

3. Additions to the concept of potential pot odds in poker

There are other points and subtleties that mathematically need to be taken into account when deciding to make a call, guided by the potential chances of the pot.

Potential chances of the bank on the pot flop

When you count your equity on the flop (for example, flush draw has an 18% chance of collecting flush on the turn), you would also do well to consider the likelihood that by paying one opponent's bet, you will be able to see two streets if the villain checks on the turn. Thus, with some frequency over the the long run, you will have 36% equity, not 18%. 

Playing without a position

Suppose you are playing a turn without a position and you do not have a proper pot chance for a call with your draw, but you have a favorable potential pot chance. It should be understood here that without a position, it will be more difficult for you to get a vellya from your opponent if your draw closes. You will have to do a dunk bet on the vellya because your check will often result in a check in return from your opponent. And such a line from your side looks quite readable. 

Compare this to a game with a closed draw at position: 

• If your opponent makes a check, you can bet on the value.
• If your villain bet, you will be able to decide whether to raising you or call with your completed combination.
• If the draw does not gather and the villain makes a check, you have the opportunity for a bluff bet, which is also profitable in many situations. 

To better understand this, read the article: fold equity in poker and the mathematics of bluff

Perhaps the villain bluffs
bluff If your villain is inclined to bluff, this circumstance can help you draw a call with the pot on the potential chances of the bank. You have more opportunities to win the pot, since even if your draw does not close, you can just drive a pair that wins at the showdown. And sometimes you will win even on the higher card. 

Which villain opponent is against you
If a good player is against you and your draw closes, he will pay you much less chips in the the long run than a weak player. Therefore, the strength of the opponent is also taken into account in deciding whether to call or not according to the potential chances of the pot. 

How obvious is your draw
If your draw is well disguised (for example, a double gutshot), your opponent will have more incentives to bet on a wide range when you catch your outs. The fact is that it will be more difficult for your opponent to put you on the draw-hand. Conversely, if your flush draw closes (usually the most obvious draw), then some opponents may stop betting for fear that you might improve your hand. Therefore, when calculating the bank's potential chances, always consider how obvious your draw is for your opponent. 

Draw draw draw through raise play
It is often more profitable to play the hand aggressively rather than passively, equalizing the opponent's bet. This happens due to the presence of fold equity in each aggressive action.

Aggression in poker is very important. But here it should be borne in mind that perhaps, in response to your aggression, the player will go all-in and generally will not give you a chance to see the cards coming out on the following streets. Therefore, this move should be used either with a weak draw, which is not a pity, or with a very strong draw, with which we are ready to play all the chips.

4. How to learn to use implied odds in the game

The ability to roughly assess your chances of winning (equity) and understand what pot odds (sub-odds) the villain gives us when making a bet is a key mathematical skill in Texas Hold 'em. There is no need to try to deliberately count every hand in your mind. This information is rather intuitive and experienced. But in order for it to be absorbed by your mind, and for your intuitive strategic decisions and calculations to become more accurate and profitable, for some time you need to pay maximum attention to these mathematical categories in the game and try to calculate something in your mind.